Hello, Shinn!
I'll do the "only if" part . . .For integers and , show that: .
Since
Since
Then: .
Hence: .
Therefore: .
Hi
I don't see any very easy proof.
Maybe you can do that using a contraposition proof:
assume doesn't divide nor i.e. there are integers such that and
Then where
therefore i.e. does not divide
To prove compute all squares in
Another way to show that would be to say that is a factorial ring, that is an odd prime and so it is irreducible in and as a consequence